Existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric spaces

Abstract

In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫ a b K 1 (t,r,x(r)) dr, x (t) = ∫ a b K 2 (t,r,x(r)) dr, where a, b ∈ℝ with a < b, x ∈C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.